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By Giorgio Ausiello, Stefano Leonardi, Alberto Marchetti-Spaccamela (auth.), Giancarlo Bongiovanni, Rossella Petreschi, Giorgio Gambosi (eds.)

The papers during this quantity have been awarded on the Fourth Italian convention on Algorithms and Complexity (CIAC 2000). The convention came about on March 1-3, 2000, in Rome (Italy), on the convention heart of the collage of Rome \La Sapienza". This convention was once born in 1990 as a countrywide assembly to be held each 3 years for Italian researchers in algorithms, facts constructions, complexity, and parallel and dispensed computing. as a result of a signi cant participation of international reaserchers, ranging from the second one convention, CIAC advanced into a world convention. based on the decision for papers for CIAC 2000, there have been forty-one subm- sions, from which this system committee chosen 21 papers for presentation on the convention. every one paper was once evaluated through at the very least 3 application committee individuals. as well as the chosen papers, the organizing committee invited Giorgio Ausiello, Narsingh Deo, Walter Ruzzo, and Shmuel Zaks to provide plenary lectures on the convention. we want to exhibit our appreciation to the entire authors of the submitted papers, to this system committee individuals and the referees, to the organizing committee, and to the plenary teachers who permitted our invitation.

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The quality of DCMST(10) obtained by the IR technique using the two different edge replacement methods, ERM1 and ERM2, is shown in Figure 6. The diagram shows the weight of the computed DCMST(10) as a multiple of the weight of the unconstrained MST. The time taken by the algorithm using ERM1 and ERM2 to obtain DCMST(10) is shown in Figure 7. As expected, ERM2 out-performs ERM1 in time and quality. In addition, ERM1 uses more memory than ERM2, because the size of MID when we use ERM1 is significantly larger than its size when ERM2 is used.

Given a physical network, the problem is to design these paths optimally. Each such design forms a layout of paths in the network, and each connection between two nodes must consist of a concatenation of such virtual paths. The smallest number of these paths between two nodes is termed the hop count for these nodes, and the load (or congestion) of a layout is the maximum number of virtual paths that go through any (physical) communication line. The two principal parameters that determine the optimality of the layout are the maximum congestion of any communication line and the maximum hop count between any two nodes.

Note that the algorithm will fail only when we try to remove edges incident to the end-points of the longest paths in the spanning tree. Also note that we move away from the center of the tree every time we go through the entire set MID without finding a good replacement edge, and we return to the center of the spanning tree every time we succeed. 25 20 DCMST(3) 15 ERM1 10 ERM2 DCMST(4) 5 0 100 200 300 400 500 Number of Nodes (n) Fig. 6. Quality of DCMST(10) obtained using two different edge-replacement methods.

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